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401-5003-58L DR D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-PHYS , D-BIOL , D-ERDW , D-GESS , D-ITET , D-ARCH , D-CHAB

Ricci Flow and the Sphere Theorem

Lecturers: Prof. Dr. Simon Brendle
VVZ CR n/a

Last Updated: 2026-02-05 15:25:11

Abstract

"Nachdiplomvorlesung"

Content

The Ricci flow, introduced by R. Hamilton in 1982, following earlier work by Eells and Sampson, deforms a Riemannian metric with a speed given by the negative of the Ricci tensor. This process often deforms the initial metric to a canonical metric. For example, a by now classical theorem of Hamilton asserts that a three-manifold of positive Ricci curvature is deformed to a spherical space form under the flow. In this lecture series, I will describe the proof of this result, and discuss to what extent the ideas involved in the proof carry over to higher dimensions. I will begin with a discussion of the evolution of curvature under Ricci flow. Later, I plan to go over a paper by C. Böhm and B. Wilking on manifolds with 2-positive curvature operator. I will also discuss the notion of positive isotropic curvature, and describe my recent joint work with R. Schoen on the Differentiable Sphere Theorem.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
DR

Examination

Type
no performance assessment

Course Components

Type Title Time & Place Hours
lecture Ricci Flow and the Sphere Theorem
  • Tue 10:15-12:00 (HG G 43)
  • Wed 10:15-12:00 (HG G 43)
  • 14.10 Date 10:15-12:00 (HG G 43)
2 h weekly

Offered In